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A little more Quicksorting
by phil | Mar 15, 2012 - 04 p.m.


This has been quite a week. I've made the decision to take a new job and move my fiancee and myself to Buffalo from Brooklyn. We think that moving there will give us a better opportunity to live the lifestyle we want. A shorter commute, more space and proximity to family are among a whole host of reasons we've decided to do it. It was a difficult decision, and we'll both miss a lot of things about Brooklyn, but I think its for the best, even though I feel a little overwhelmed right now.

Anyway, I was poking through my work computer to see if there was any code that I didn't want to leave behind, and I found something that played off last week's interest in Quicksort. It was a piece of code that I had written when I first taught myself the algorithm. And, unlike most of your old code you run into, this was more nicely written than what I wrote just recently.
#what I wrote last week
def quicksortLoop(set):
    if len(set) <= 1:
        return set

    high = []
    low = []
    pivot = set.pop(len(set) / 2)

    for i in set:
        if i >= pivot:
            high.append(i)
        else:
            low.append(i)
    return quicksortLoop(low) + [pivot] + quicksortLoop(high)

#what I wrote a long time ago
def quicksort(list):
    if len(list) <= 1:
        return list;

    pivot = list.pop(len(list) / 2)
    less = [i for i in list if i < pivot]
    more = [i for i in list if i >= pivot]
    return quicksort(less) + [pivot] + quicksort(more)


Instead of looping through the set and putting values into two arrays, this implementation uses python's list comprehensions to build the more and less lists. I think this approach is much more elegant, yielding easier to read code.

This lead me to the question of whether or not the list comprehensions incurred a signifigant amount of overhead. To find out, I stripped away all the parts that distiguished the two different implementations from one another with the exception of the loop vs list comprehension pieces. Then I wrote some code to the run the two different function through the same paces.

from time import time
from random import randint

#function definitions here

if __name__ == "__main__":

    loopTimes = []
    compTimes = []

    for i in range(1, 1000):
        testSet = [randint(0, 100) for x in range(1000)]

        cSet = list(testSet)
        loopSet = list(testSet)

        compTime = time()
        quicksortComprehension(cSet)
        compTime = time() - compTime
        compTimes.append(compTime)

        loopTime = time()
        quicksortLoop(loopSet)
        loopTime = time() - loopTime
        loopTimes.append(loopTime)

    print "Avg with loop: ", sum(loopTimes)/1000
    print "Avg with list comprehension: ", sum(compTimes)/1000
What this is does is sort a thousand lists, each containing a thousand numbers between one and one hundred, using both sorting functions. It counts the time each function takes on each list, and then calculates an average.

The results are sort of interesting.
[snpxw@PWadeiMAC:random-bits ]$ python quicksortTimer.py 
Avg with loop:  0.00623641085625
Avg with list comprehension:  0.0061008477211
List comprehensions beat the loop every time, which is the opposite of what I expected. I'll speculate that the difference is either some internal optimization python makes for list comprehensions, or the pre-allocation of the low and high arrays in the loop version. I'm going to have to do a bit more research about what happens inside python to figure it out.

Regardless, the difference is negligible. Even if the list being sorted was five thousand times larger (that is, five million elements), the difference in the two implementations would be about 0.5 seconds. Not really enough to bother most people.

(The full code from this post is here.)